in this module we will be trying to
define what exactly a complex system is
before we start we should note that
there is no formal definition for what a
complex system is and thus there remains
many different perspectives and opinions
on the subject what we present here is
just a working definition
firstly a complex system is a special
class of system a system is simply a set
of parts called elements and a set of
connections between these parts called
relations these parts can be ordered or
unordered an unordered system is simply
a set of things because there is no
specific structure or order we can
describe a set simply by listing all of
its elements and their properties so a
pile of stones on the ground is an
example of an unordered set as there is
no pattern or order to the system we can
only describe it by describing the
properties of each element in isolation
and then adding them all up with the
whole set being nothing more than the
sum of its individual parts
if in contrast through the relations
these parts are ordered in a specific
way then they can function together as
an entirety and out of these parts
working together we get the emergence of
a global pattern of organization that is
capable of functioning as a coherent
whole for example if all the parts in
our car are arranged in a specific way
then we will have the global
functionality of a vehicle of
transportation or out of the specific
arrangement of billions of cells and the
different specialized organs that make
up our body we get the emergence of a
global system that enables us to operate
as an entire organism so that is the
basic model of the system it consists of
elements and relations when those
elements work together we get the
emergence of a new level of organization
now let's start adding complexity to
this probably the only property that
will be in all definitions of a complex
system is that they consist of many
parts many parts that are distributed
out without centralized control
organization is formed out of the local
interactions between the parts through a
process of self-organization that gives
rise to the emergence of new levels of
organization with the phenomenon of
emergence that we were previously
discussing a whole new level to the
system has developed which then starts
to interact with other systems in its
environment the result being that new
patterns of organization developed and
once again we get the emergence of
another level of organization and so on
people form part of social groups that
form part of broader society which in
turn forms part of humanity the point to
take away here is that these systems
have a hierarchical structure this is a
pervasive phenomenon in our world
elements are nested inside of subsystems
which in turn form part of larger
systems and so on all complex systems
have this multi-dimensional property to
them they are composed of many elements
on many different scales with all of
these levels affecting each other a
business is part of a local economy
which is part of a national economy
which in turn is part of a global
economy each is interconnected and
interdependent with the others we cannot
fully isolate one component or reduce
the whole thing to one level and this is
a primary source of complexity so this
is our first property to a complex
system many different parts that are
distributed out with local interactions
and self-organization giving rise to new
emergent levels on different scales
next interdependence and non-linearity
the parts to a complex system are highly
interdependent in this interdependence
creates non-linearity almost all well
formulated definitions for complex
systems involve the term non-linearity
it is a continuously recurring and
pervasive theme non-linearity arises
from the fact that when we put two or
more things together the result may not
necessarily be a simple addition of each
elements properties in isolation in
contrary we may get a combined effect
that is greater or less than the simple
sum of each part because of their
interdependent nature examples of this
might be two sound waves that are
perfectly out of sync cancelling each
other out through noise interference or
the division of labor as can be seen in
many human and insect communities
resulting in synergies which means the
output will be far greater than what
individuals could accomplish in
isolation
due to what are called feedback loops
nonlinear systems may grow or decay at
an exponential rate these periods of
rapid change are defined as phase
transitions
thus complex systems are known to be
able to shift or flip into whole new
regimes within very brief periods of
time some small change in input value to
the system can through feedback loops
trigger a large systemic effect this is
called sensitivity to initial conditions
and it is the central idea within chaos
theory examples of this butterfly effect
can be seen in financial crises and the
collapse of ecosystems such as coral
reefs
next connectivity many definitions for
complex systems involve dense or high
levels of interconnectivity between
components as we turn up the degree of
connectivity it becomes the nature and
structure of these connections that
define the system as opposed to the
properties of its components how are
things connected and what is connected
to what become the main questions at
some critical level of connectivity the
system stops being a set of parts and
becomes a network of connections and it
is now all about how things flow in this
network networks are the Trudy Amma tree
of complex systems in this connectivity
reshapes our traditional 3-dimensional
Euclidean conception of space in complex
systems like the global air
transportation system or the financial
system or the Internet space is
redefined in terms of topology created
by connectivity what matters is your
position in the network structure and
your degree of connectivity connectivity
again leads us into the world of
complexity as the number of relations
between elements can grow in an
exponential fashion if we take just a
handful of elements they can become
connected and possibly thousands or even
millions of different ways
lastly autonomy and adaptation whether
we are talking about a flock of birds
the internet or our global economy there
is no top-down centralized mechanism for
coordinating the whole system within
complex systems elements have a degree
of autonomy often through their capacity
to adapt to their local environment
according to their own set of
instructions without centralized
coordination and with a degree of
autonomy elements can synchronize their
states locally or cooperate resulting in
the emergence of patterns of
organization from the bottom up with
autonomy and adaptation also comes the
capacity for a variety of different
responses for any given phenomenon
meaning complex systems are often
heterogeneous with high levels of
diversity ecosystems and multicultural
societies are good examples of this
without centralized coordination complex
systems develop on the macroscale
through a process of evolution elements
within complex adaptive systems are
subject to the evolutionary force of
selection where those that are best
suited to that environment are selected
and replicated while others are not
products are subjected to selection
within a market environment in
democracies politicians are subject to
selection by voters and creatures and
ecosystems are subjected to natural
selection through competition in such a
way the whole macro scale system manages
to adapt to its environment without
centralized coordination and develop to
exhibit higher levels of both
differentiation and integration the
greater the autonomy and capacity for
adaptation that elements have the more
complex the system we are dealing with
in summary we have been trying to lay
down a basic working definition for a
complex system while remembering that
there is no formal consensus on the
subject we firstly talked about how a
complex system is a special class of
system we defined a system as a set of
elements and the relations between them
we saw how when these parts are arranged
in a specific order for them to function
as an entirety we get what is called the
process of emergence whereby a new level
of organization emerges we then began to
add complexity to our model of a system
by defining it as a product of four
primary parameters firstly talking about
the number of elements and different
levels to the hierarchy within our
system we then discussed non-linearity
as another dimension to complexity were
non-additive interactions and feedback
loops over time can give us exponential
relations between the input and output
to a system and lead to phase
transitions we also talked about
connectivity as another driver of
complexity as heightened connectivity
within complex systems means they often
appear to us as networks
lastly we discussed how autonomy and
adaptation enables self-organization in
the process of evolution that shapes
complex systems on the macro scale